A1257278342CsTnl - PowerPoint PPT Presentation

Title: A1257278342CsTnl


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Statistical Decision Making

• Analysts must often make decisions about some
  condition in the real world.
• Assume that you have finished your MA in policy
  studies and have been hired as the environmental
  affairs officer for the city of Morgantown.
• You must make the following assessment
• Does the water supply in Morgantown comply with
  safe drinking water standards?

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Hypothesis Testing
We can decide the facility is incompliance. Or We
can decide the facility is in Violation. (not in
compliance)
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If we decide The facility is in compliance and
it is. Or We decide the facility is in violation
and it is. Then we are fine. But often were
not correct. We make mistakes. Statistics gives
us some rules to reduce the likelihood of making
these mistakes.
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Example of a statistical test

• In order to test the facilities water we will
  collect several bottles of water at different
  times.
• We take this sample
• (Do not be confused by the chemistry. Each
  bottle of water is a sample to the chemist, while
  all of the separate bottles of water are the
  sample to the statistician.)
• And we calculate the average amount of the
  pollutant e.g. lead.

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The average of the samples is thus X Our
hypothesis is thus X ? the standard for
lead Because we will say that the standard
actually refers to a population distribution with
a mean equal to the standard, we can restate this
is conventional statistical terms X ? ?
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Hypotheses

• The hypothesis is
• The facility is in violation.
• Sometimes referred to as The alternate
  hypothesis.
• The null hypothesis is
• The facility is in compliance.
• In this instance, you want to be able to reject
  the alternate hypothesis, or more properly, fail
  to reject the null hypothesis.

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Decision
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Decision
In Compliance
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Decision
In Compliance
In Violation
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Decision
In Compliance
In Violation
Real World
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Decision
In Compliance
In Violation
In Compliance
Real World
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Decision
In Compliance
In Violation
In Compliance
Real World
In Violation
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Decision
In Compliance
In Violation
In Compliance
Real World
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
In Compliance
Real World
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
In Compliance
Correct
Real World
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
In Compliance
Correct
Real World
Correct
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
Incorrect
In Compliance
Correct
Real World
Correct
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
Incorrect
In Compliance
Correct
Real World
Correct
Incorrect
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
Incorrect Prob. ?
In Compliance
Correct
Real World
Correct
Incorrect
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
Incorrect Prob. ?
In Compliance
Correct Prob. 1-?
Real World
Correct
Incorrect
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
Incorrect Prob. ?
In Compliance
Correct Prob. 1-?
Real World
Correct
Incorrect Prob. ?
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
Incorrect Prob. ? (Type I error)
In Compliance
Correct Prob. 1-?
Real World
Correct
Incorrect Prob. ?
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
Incorrect Prob. ? (Type I error)
In Compliance
Correct Prob. 1-?
Real World
Correct
Incorrect Prob. ? (Type II error)
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
Incorrect Prob. ? (Type I error)
In Compliance
Correct Prob. 1-?
Real World
Correct Prob. 1-?
Incorrect Prob. ? (Type II error)
In Violation
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Decision
In Compliance Do not reject H0
In Violation Reject H0
Incorrect Prob. ? (Type I error)
In Compliance
Correct Prob. 1-?
Real World
Correct Prob. 1-? (Power of the test)
Incorrect Prob. ? (Type II error)
In Violation
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